Stair Angle Calculator
Enter rise and run to get the exact stair angle in degrees and slope — and see instantly whether it falls in the comfortable 30–37° range.
Finished floor to finished floor.
Stairs Calc rounds to a whole number of equal risers and keeps them within code.
The depth you step on, not counting the nosing.
Top of the rail above the nosing line. Codes target 34–38".
A guard fills the side with your chosen infill — balusters, glass, cable, or horizontal bars. Renders live in 3D and is included in the .obj export.
Advanced inputs
Open risers leave a gap between treads — drawn live in the diagram. Some codes (ADA) require closed risers.
Steps (risers)
16
15 treads
Riser height
7 3/16"
183 mm
Tread run
11"
279 mm
Stringer length
16' 8 15/16"
5.104 m
Stair angle
33.2°
Very comfortable
Total run
13' 8 3/4"
4.185 m
Min stairwell opening
10' 11 13/16"
3.348 m
Recommended board
2x12
throat 5 1/4"
Board to buy
17' 8 15/16"
5.409 m
Comfort
Very comfortable
- Blondel pass
- Rise + Run pass
- Ideal angle pass
Cut list & framing square
Materials
| Item | Qty | Detail |
|---|---|---|
| Stringers | 3 | 2x12 cut to board length |
| Treads | 15 | tread depth 304 mm × 914 mm wide |
| Risers | 16 | riser height 183 mm × 914 mm wide |
| Fasteners | 180 | structural screws / nails (≈4 per tread-to-stringer joint) |
Framing-square settings
- Rise on tongue
- 7 3/16"
- Run on body
- 11"
- Recommended board
- 2x12
- Throat
- 5 1/4"
- Board length
- 17' 8 15/16"
- Stringers
- 3
Per-step running measurements
| Step | Cumulative rise | Cumulative run |
|---|---|---|
| 1 | 7 3/16" | 11" |
| 2 | 14 3/8" | 21 15/16" |
| 3 | 21 9/16" | 32 15/16" |
| 4 | 28 3/4" | 43 15/16" |
| 5 | 35 15/16" | 54 15/16" |
| 6 | 43 1/8" | 65 7/8" |
| 7 | 50 5/16" | 76 7/8" |
| 8 | 57 1/2" | 87 7/8" |
| 9 | 64 11/16" | 98 7/8" |
| 10 | 71 7/8" | 109 13/16" |
| 11 | 79 1/16" | 120 13/16" |
| 12 | 86 1/4" | 131 13/16" |
| 13 | 93 7/16" | 142 13/16" |
| 14 | 100 5/8" | 153 3/4" |
| 15 | 107 13/16" | 164 3/4" |
| 16 | 115" | 175 3/4" |
Cut the bottom riser shorter by 1" so every finished riser stays equal.
Save & compare designs Show Hide
Save the stair you're looking at, tweak the inputs, save another, then compare them side by side — comfort, code, and key dimensions at a glance.
Estimate the cost $1,139–$1,709
| Stringers (3) | $176 |
| Treads (15) | $270 |
| Risers (16) | $144 |
| Fasteners & hardware | $25 |
| Railing | $335 |
| Labor | $475 |
Low
$1,139
Estimate
$1,424
$89/step
High
$1,709
Rough order-of-magnitude only. Lumber, fastener and labor prices swing by region and season — the low–high band reflects that spread. For a line-item breakdown with editable prices, open the stairs cost calculator.
What is the angle of stairs?
Stair angle is the arctangent of rise over run: angle = atan(rise ÷ run). A comfortable staircase falls between 30° and 37°; the canonical 7″ rise with an 11″ run lands at about 32–33°. Steeper than ~42° is usually outside residential code.
- Comfortable range
- 30°–37°
- Typical (7″/11″)
- ≈ 32.5°
- Formula
- atan(rise ÷ run)
What angle should stairs be?
Stair angle is simply atan(rise ÷ run) — the pitch of one step. The comfortable range is 30–37°, and the most comfortable stairs sit right in the middle: a 7″ rise over an 11″ run is about 32.5°. (You’ll see “37°” quoted as the 7-11 angle online — that’s wrong; it comes from using the wrong run.)
- Below 30° — shallow and space-hungry, but very easy.
- 30–37° — the comfortable, code-friendly range for everyday stairs.
- 37–45° — steep; acceptable for some uses but tiring and harder to descend.
- OSHA workplace stairs allow 30–50°; steeper than 50° becomes a ship’s ladder.
Switch the calculator to Workplace (OSHA) to check against the 30–50° band, and watch the angle arc in the diagram update as you change the rise and run. To set those numbers for a target angle, use the stair rise and run calculator.
Worked example — the angle of a 16-riser flight
Take the canonical staircase: a 9′‑7″ total rise split into 16 equal risers gives a 7³⁄₁₆″ riser, paired with an 11″ run. The angle is the arctangent of one step’s rise over its run:
angle = atan(182.6 mm ÷ 279 mm) = atan(0.654) ≈ 33.2°
That sits squarely in the 30–37° comfort band and inside every residential code, which is why it is the example the rest of Stairs Calc is built around. Use the per-step rise and run, not the totals: total rise ÷ total run gives a steeper figure because the total run is measured nosing-to-nosing and the top tread laps the floor, so the per-step pitch is the one that matters for comfort.
Stair angle reference
Every angle below is atan(rise ÷ run) on a common step, so you can read off the pitch a given rise-and-run pair produces before you build:
| Step (rise · run) | Angle | Verdict |
|---|---|---|
| 6″ rise · 13″ run | 24.8° | Very shallow — easy, but eats floor space |
| 7″ rise · 11″ run (7‑11) | 32.5° | The comfort sweet spot |
| 7³⁄₁₆″ rise · 11″ run | 33.2° | The 16‑riser worked example below |
| 7¾″ rise · 10″ run (IRC limits) | 37.8° | Steepest a code stair can be |
| 8″ rise · 9″ run | 41.6° | Over the comfortable max — steep and tiring |
Common stair-angle mistakes
- Quoting 37° as the 7-11 angle. A real 7″ rise over an 11″ run is 32.5°. The 37° figure comes from a 7″ run, which is a far steeper stair than 7-11.
- Using total rise ÷ total run. That overstates the pitch. The angle is set by one step’s rise and run, not the whole-flight totals.
- Mixing up rise and run. atan(run ÷ rise) gives the complement of the real angle — a 32.5° stair would read as 57.5°. Rise goes on top of the fraction.
- Designing to OSHA in a home. The 30–50° workplace band is far steeper than a comfortable house stair; for living space, stay in the 30–37° range.
- Forcing an angle into a tight space. Picking a steep angle to save floor area usually pushes the riser over the code maximum — size the rise and run first, then read the angle off, not the other way round.
Frequently asked questions
What is a comfortable stair angle?
A comfortable staircase falls between 30° and 37°. A 7‑11 stair sits right in the middle at about 32.5°.
What is the maximum stair angle?
For everyday stairs the comfortable maximum is about 37°. Workplace stairs under OSHA may be steeper — up to 50° — and ship or alternating‑tread stairs steeper still, but those are special cases, not normal building stairs.
How do you calculate the angle of stairs?
The angle is the arctangent of the rise over the run: angle = atan(rise ÷ run). For a 182.6 mm rise and 279 mm run that is atan(182.6 ÷ 279) ≈ 33.2°.
What angle is a 7‑11 stair?
A 7″ rise over an 11″ run is atan(7 ÷ 11) ≈ 32.5°, not the "37°" often quoted online — that figure comes from using the 7″ rise with a 7″ run, which is far steeper than a real 7‑11 step.
Related stair calculators
Written by the Stairs Calc editorial team. Methodology and code references: see our methodology.
Built and maintained by builders, drafters and engineers who plan stairs for a living — every code limit is transcribed from the published standard and cited to its exact section.
Last reviewed 2026-06-20 against IRC 2021/2024
Stairs Calc gives accurate geometry and checks it against published building-code limits, but results are estimates for planning. Codes are adopted and amended locally and change over time. Always confirm dimensions against your local adopted code and a licensed professional before you build.